Question: Rewrite as a simplified fraction. ${3.\overline{21} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 321.2121...\\ 1x &= 3.2121...\end{align*}}$ Subtracting the two equations, we have: ${99x = 318}$ ${x = \dfrac{318}{99}} $ ${x = \dfrac{106}{33}} \text{or} {3 \dfrac{7}{33}}$